mesh doesn't follow armature correctly - bones outside the mesh
I think the problem is that your weights, give influence to the movement of that part of the mesh (an arm of the creature) to two different bones:



So, afaik, the end of the arm, being influenced by two different bones, is a "compromise" (or more properly a "blend") of the position of the two involved bones. 

I roughly tried to correct the weights of the first image:


and you see the mesh now behaves better, hopefully?

(btw the other arm of your model already has a similar setup and the mesh moves like expected)